Median for grouped data is given by
\[L+(\frac{\frac{N+1}{2}-(F+1)}{f})*h\]
where, L = lower limit of median class
N= total number of data items
F= cumulative frequency of class immediately preceding the median class.
f= frequency of median class
h = width of median class
For example-
Consider the following table giving the marks obtained by students in an exam.
Marks Range f -No of students cumulative frequency
0-20 2 2
20-40 3 5
40-60 10 15
60-80 15 30
80-100 20 50
Solution
Here N=50 L=60 F=15 f=15 h=20
\[60+(\frac{\frac{50+1}{2}-(15+1)}{15})*20\]=72.66
Hence Median marks of the class is approximately 72.667
This also means half the student got less than 72.667 and half got more than 72.667
